WASHINGTON — The partisan political divide over the potential nomination of UN Ambassador Susan Rice to be secretary of state intensified on Sunday with Republicans questioning her fitness for the job and Democrats defending her.

Republican senators said they remain deeply concerned over Rice’s statements about the Sept. 11 attack on the US diplomatic post in Benghazi, Libya, and suggested her motive was to help President Obama’s reelection chances.

Rice has conceded in private meetings with lawmakers that her initial account — that a spontaneous demonstration over an anti-Muslim video produced in the United States triggered the attack — was wrong, but she has insisted she was not trying to mislead the American people.

That account was provided by intelligence officials who have since said their understanding of the attack evolved as more information came to light.

Appearing on Sunday talk shows, two of Rice’s fiercest Republican critics, Senators Kelly Ayotte of New Hampshire and Lindsey Graham of South Carolina, said Rice’s account went beyond talking points that the intelligence agencies gave her. For one, they noted she had said that security at the Benghazi mission was ‘‘strong, substantial, and significant.’’

That statement ‘‘was not supported by the talking points,’’ Ayotte said in an interview on CNN’s “State of the Union.’’ She said that Rice was privy to more than just the unclassified material she discussed on television, including secret intelligence briefings that pointed to Al Qaeda involvement in the attack.

‘‘I think her story on 16th of September was a political story designed to help the president . . . and she should be held accountable for that,’’ Graham said on CBS’s “Face the Nation.’’ He
said that Rice’s comments were ‘‘a treasure trove of misleading statements that have the effect of helping the president.’’

Rice met with both Graham and Ayotte last week to explain the situation, but Graham said Rice ‘‘didn’t do herself much good’’ in the encounter.

Ayotte sits on the Senate Armed Services Committee alongside Graham and Senator John McCain of Arizona.

She has increasingly used a growing partnership with the two senior members to become one of the GOP’s most visible figures on national security issues.

Senator Bob Corker, Republican of Tennessee, said on NBC’s “Meet the Press’’ that he and others questioned whether Rice was acting as a diplomat or a ‘‘political operative.’’

But Democrats said Rice is being unfairly victimized for repeating erroneous talking points circulated by the intelligence community.

fierce critic

‘‘Nothing that I have heard, in my mind, would disqualify her’’ from being secretary of state, said Senator Mark Warner, Democrat of Virginia.

Senator Claire McCaskill. Democrat of Missouri, said Sunday that what’s happening to Rice is ‘‘terribly unfair’’ and a brighter light should be
shined on the role of former CIA chief David Petraeus and his agency.

‘‘The talking points came from the intelligence community, yet you don’t hear one criticism of David Petraeus,’’ McCaskill said. “It was his shop that produced the talking points that Susan Rice talked about. . . . Is there a double standard here? It appears to most of us that there is. A very unfair one.

‘‘It is terribly unfair that she should be the scapegoat for this when really the failures ought to be at the lap of the head of the intelligence community that produced these talking points, but none of these guys will say a word about David Petraeus.’’

Diane Feinstein, a California Democrat who chairs the Senate Intelligence Committee, said she thought one of the problems was the distribution of unclassified talking points and suggested that incomplete information should not be put out, particularly if it differed from classified material.

All the lawmakers said they believed that inadequate security at the mission must be investigated and corrected so that Benghazi is not repeated.

Representative Mike Rogers, a Michigan Republican who chairs the House Intelligence Committee, said the lack of security constituted ‘‘gross negligence.’’

While Obama has made no final decisions on vacancies in his Cabinet, he is considered almost certain to nominate Rice.